信号处理导论（英）Chapter Four FIR Filtering and Convolution.pptVIP

Chapter Four: FIR Filtering and Convolution 4.1.1 Convolution 4.1.2 Direct Form 4.1.3 Convolution Table 4.1.4 LTI Form 4.1.5 Matrix Form 4.1.6 Flip-and-Slide Form 4.1.7 Transient and Steady-State Behavior * * 1.Block Processing: 应用举例：a. FIR filtering of finite-duration signals by convolution b. fast convolution of long signals c. DFT/FFT spectrum computation d. speech analysis and synthesis e. image processing 2.Sample Processing:(state-space realizations of LTI filters) 应用举例：a. real-time filtering of long signals b. digital audio effects processing c. digital control systems d. adaptive signal processing In this chapter,we consider block processing and sample processing methods for FIR filtering applications. 1) block processing methods for FIR filtering We discuss the computational aspects of the convolution equations (3.3.2) or (3.3.3) as they apply to FIR filters and finite-duration inputs. Various equivalent forms of convolution： 1. Direct form 2. Convolution table 3. LTI form 4. Matrix form 5. Flip-and-slide (反转滑动) form 6. Overlap-add block convolution form 2) sample processing methods for FIR filtering Then,we go on to discuss sample-by-sample processing methods for FIR filters and discuss block diagram realization which provide a mechanization of the sample processing algorithms . 1) the duration of the data record P.125图 2）输入信号 3）the direct and LTI forms of convolution  4.1 Block Processing Methods *当输入x(n)和h(n)都是有限长因果序列时确定direct form 的求和范围： * 输出数据块的长度： * Advantages : leads directly to block diagram realizations of the filter and the corresponding sample-by-sample processing algorithm . (P.124) 通过这一节的学习大家关键要掌握求卷积和的求和范围的通用方法 Fig.4.1.2 Example 4.1.1